Riesz sequences and arithmetic progressions

Itay Londner, and Alexander Olevskiĭ. "Riesz sequences and arithmetic progressions." Studia Mathematica 225.2 (2014): 183-191. <http://eudml.org/doc/286169>.

@article{ItayLondner2014,
abstract = {Given a set of positive measure on the circle and a set Λ of integers, one can ask whether $E(Λ) := e^\{iλt\}_\{λ∈Λ\}$ is a Riesz sequence in L²(). We consider this question in connection with some arithmetic properties of the set Λ. Improving a result of Bownik and Speegle (2006), we construct a set such that E(Λ) is never a Riesz sequence if Λ contains an arithmetic progression of length N and step $ℓ = O(N^\{1-ε\})$ with N arbitrarily large. On the other hand, we prove that every set admits a Riesz sequence E(Λ) such that Λ does contain arithmetic progressions of length N and step ℓ = O(N) with N arbitrarily large.},
author = {Itay Londner, Alexander Olevskiĭ},
journal = {Studia Mathematica},
keywords = {Riesz sequences; arithmetic progressions},
language = {eng},
number = {2},
pages = {183-191},
title = {Riesz sequences and arithmetic progressions},
url = {http://eudml.org/doc/286169},
volume = {225},
year = {2014},
}

TY - JOUR
AU - Itay Londner
AU - Alexander Olevskiĭ
TI - Riesz sequences and arithmetic progressions
JO - Studia Mathematica
PY - 2014
VL - 225
IS - 2
SP - 183
EP - 191
AB - Given a set of positive measure on the circle and a set Λ of integers, one can ask whether $E(Λ) := e^{iλt}_{λ∈Λ}$ is a Riesz sequence in L²(). We consider this question in connection with some arithmetic properties of the set Λ. Improving a result of Bownik and Speegle (2006), we construct a set such that E(Λ) is never a Riesz sequence if Λ contains an arithmetic progression of length N and step $ℓ = O(N^{1-ε})$ with N arbitrarily large. On the other hand, we prove that every set admits a Riesz sequence E(Λ) such that Λ does contain arithmetic progressions of length N and step ℓ = O(N) with N arbitrarily large.
LA - eng
KW - Riesz sequences; arithmetic progressions
UR - http://eudml.org/doc/286169
ER -